A nanowire (NW) structure provides an alternative scheme for deep ultraviolet light emitting diodes (DUV-LEDs) that promises high material quality and better light extraction efficiency (LEE). In this report, we investigate the influence of the tapering angle of closely packed AlGaN NWs, which is found to exist naturally in molecular beam epitaxy (MBE) grown NW structures, on the LEE of NW DUV-LEDs. It is observed that, by having a small tapering angle, the vertical extraction is greatly enhanced for both transverse magnetic (TM) and transverse electric (TE) polarizations. Most notably, the vertical extraction of TM emission increased from 4.8% to 24.3%, which makes the LEE reasonably large to achieve high-performance DUV-LEDs. This is because the breaking of symmetry in the vertical direction changes the propagation of the light significantly to allow more coupling into radiation modes. Finally, we introduce errors to the NW positions to show the advantages of the tapered NW structures can be projected to random closely packed NW arrays. The results obtained in this paper can provide guidelines for designing efficient NW DUV-LEDs.